gcse mathematics mark scheme unit 01 - statistics and

AQA Qualifications

GCSE

Mathematics Unit 1 43601H

Mark scheme

43601H

June 2015

Version 1: Final mark scheme

Mark schemes are prepared by the Lead Assessment Writer and considered, together with the

relevant questions, by a panel of subject teachers. This mark scheme includes any amendments

made at the standardisation events which all associates participate in and is the scheme which was

used by them in this examination. The standardisation process ensures that the mark scheme covers

the students’ responses to questions and that every associate understands and applies it in the same

correct way. As preparation for standardisation each associate analyses a number of students’

scripts: alternative answers not already covered by the mark scheme are discussed and legislated for.

If, after the standardisation process, associates encounter unusual answers which have not been

raised they are required to refer these to the Lead Assessment Writer.

It must be stressed that a mark scheme is a working document, in many cases further developed and

expanded on the basis of students’ reactions to a particular paper. Assumptions about future mark

schemes on the basis of one year’s document should be avoided; whilst the guiding principles of

assessment remain constant, details will change, depending on the content of a particular

examination paper.

Further copies of this Mark Scheme are available from aqa.org.uk

Copyright © 2015 AQA and its licensors. All rights reserved. AQA retains the copyright on all its publications. However, registered schools/colleges for AQA are permitted to copy material from this booklet for their own internal use, with the following important exception: AQA cannot give permission to schools/colleges to photocopy any material that is acknowledged to a third party even for internal use within the centre.

MARK SCHEME – GENERAL CERTIFICATE OF EDUCATION MATHEMATICS – 43601F – JUNE 2015

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Glossary for Mark Schemes

GCSE examinations are marked in such a way as to award positive achievement wherever

possible. Thus, for GCSE Mathematics papers, marks are awarded under various categories.

If a student uses a method which is not explicitly covered by the mark scheme the same principles

of marking should be applied. Credit should be given to any valid methods. Examiners should seek

advice from their senior examiner if in any doubt.

M Method marks are awarded for a correct method which could

lead to a correct answer.

A Accuracy marks are awarded when following on from a correct

method. It is not necessary to always see the method. This can

be implied.

B Marks awarded independent of method.

Q Marks awarded for Quality of Written Communication

ft Follow through marks. Marks awarded for correct working

following a mistake in an earlier step.

SC Special case. Marks awarded within the scheme for a common

misinterpretation which has some mathematical worth.

M dep A method mark dependent on a previous method mark being

awarded.

B dep A mark that can only be awarded if a previous independent mark

has been awarded.

oe Or equivalent. Accept answers that are equivalent.

eg, accept 0.5 as well as 2

1

[a, b] Accept values between a and b inclusive.

3.14 … Accept answers which begin 3.14 eg 3.14, 3.142, 3.149.

Use of brackets It is not necessary to see the bracketed work to award the marks.

MARK SCHEME – GENERAL CERTIFICATE OF EDUCATION MATHEMATICS – 43601H – JUNE 2015

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Examiners should consistently apply the following principles

Diagrams

Diagrams that have working on them should be treated like normal responses. If a diagram has been

written on but the correct response is within the answer space, the work within the answer space should be

marked. Working on diagrams that contradicts work within the answer space is not to be considered as

choice but as working, and is not, therefore, penalised.

Responses which appear to come from incorrect methods

Whenever there is doubt as to whether a candidate has used an incorrect method to obtain an answer, as a

general principle, the benefit of doubt must be given to the candidate. In cases where there is no doubt that

the answer has come from incorrect working then the candidate should be penalised.

Questions which ask candidates to show working

Instructions on marking will be given but usually marks are not awarded to candidates who show no working.

Questions which do not ask candidates to show working

As a general principle, a correct response is awarded full marks.

Misread or miscopy

Candidates often copy values from a question incorrectly. If the examiner thinks that the candidate has

made a genuine misread, then only the accuracy marks (A or B marks), up to a maximum of 2 marks are

penalised. The method marks can still be awarded.

Further work

Once the correct answer has been seen, further working may be ignored unless it goes on to contradict the

correct answer.

Choice

When a choice of answers and/or methods is given, mark each attempt. If both methods are valid then

M marks can be awarded but any incorrect answer or method would result in marks being lost.

Work not replaced

Erased or crossed out work that is still legible should be marked.

Work replaced

Erased or crossed out work that has been replaced is not awarded marks.

Premature approximation

Rounding off too early can lead to inaccuracy in the final answer. This should be penalised by 1 mark

unless instructed otherwise.


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Q Answer Mark Comments

1(a) Positive B1

Ignore any other description

Accept eg strong positive, weak positive correlation

1(b)

[28, 29] seen

or

40 + [24, 30]

or

[64, 70]

M1 [28, 29] may be seen on graph

[68, 69] A1

SC1 Answer [78, 79] with correct point or line(s) marked on graph

SC1 Answer [91, 92]

Additional Guidance

[28, 29] seen even with other values or different answer given M1A0

Correct working up to [68, 69] but then gives the answer 70 M1A1

68

90 or

69

90 etc M1A0

68

170 or

68

180 or

68

200 etc M1A1


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2(a)

Suitable hypothesis Q1

Strand (i)

eg Girls are more likely to study

Economics

More boys study Economics

Girls are less likely to study

Economics than boys

Additional Guidance

Must mention girls/ boys and studying Economics

Must be a suggested outcome and not a question

Condone a correct hypothesis followed by a reason why it may be true

May start ‘I think’, ‘I predict’, ‘I believe’ and condone ‘should be’

Condone ‘home economics’

2(b)

Two-way table with boys/ girls as row/

column and Yes/ No as column/ row B2

oe

B1 boys/ girls or Yes/ No

B0 questionnaires intended for

individuals to complete

Additional Guidance

Condone a list where all four options can be worked out ie you can tell how many: (1) boys planning E, (2) boys not planning E, (3) girls planning E, (4) girls not planning E

This may also be seen as two separate lists/ tally charts

Condone questions as headings

Ignore any attempt to fill in cells and allow any extra rows/columns eg Don’t know or Frequency

If the student gives a data collection sheet and a questionnaire, ignore the questionnaire

Yes/ No could be indicated by a tick or cross


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3(a) 9 : 5 : 6 B1

3(b)

3000

6000× 100 or

1800

6000× 100 or

1200

6000× 100

M1

oe

50

100 or

30

100 or

20

100 or

50 (white) or 30 (brown) or 20 (granary)

seen or implied

50 (white) and 30 (brown) and

20 (granary) seen or implied A1

Bar drawn in correct position and

shaded (in correct order) with correct

length, divisions and width B1ft

± 2

1small square

ft their 50, 30 and 20 with bar total 100%

Additional Guidance

Mark the graph first: a correct bar implies all 3 marks M1A1B1

Shading can be incomplete (eg only two parts shaded) as long as unambiguous or can use

labelling eg white/ brown/ granary or W/B/G

A bar drawn in the wrong order must have the correct shading M1A1B0

Correct bar with incorrect width or position M1A1B0

Condone a bar in the wrong position if it is a replacement for an incorrect bar in the right

position

30, 18, 12 (30 is for white) M0A0B0ft

Any correct section in the graph can imply M1 but you must check it is not

from incorrect working eg

6000 ÷ 3000 = 2 → 20%, 6000 ÷ 1800 = 3 → 30%, 6000 ÷ 1200 = 5 → 50%

Then bar drawn 20 : 30 : 50

Do not award M1 for brown = 30 if this method is seen but they can have

B1ft if their bar follows through from their working and totals 100

M0A0B1ft


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4

40 – 22 or 18 (female)

or

(40 – 10) ÷ 2 or 15 (male or female)

M1 Condone 18

40 or

15

30

their 18 – their 15

or

22 – their 15 or 7 (males sold)

or

(10 – (22 – their 18)) ÷ 2 or 10 4

2

M1dep Condone 7

30 or

3

30

3 A1

Additional Guidance

Answer 13 often comes from 18 – 5 so if 18 is seen award the first mark M1M0A0

3 should not be awarded full marks if it comes from an incorrect method

5(a) Point marked at (100, 0.18) B1 ± 2

1small square

5(b)

500 B2

B1 0.1 × 5000 oe

or answer of 900 or 850 or 750 or 700

or 640 or 600 or 575 or 550 or 475

Additional Guidance

A correct answer using any relative frequency from the graph or using the

average of all of them B1

Answer of 500 out of 5000 B2

Answer 500

5000 B1

The calculation for B1 may be seen in stages eg 100 per 1000 and 100 × 5 B1


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6

900 × 360 ÷ 120

or

900 × 3

or

(900 + 450) × 2

M1 oe

2700 A1

their 2700 ÷ 20 × 80 M1 oe

10 800 A1ft ft their 2700 × 4

SC2 13 500

Additional Guidance

A wrong start can still pick up the last two marks eg

900 × 120 ÷ 360 = 300

300 ÷ 2 = 150

150 × 8 = 1200

M0A0

M1A1ft

Allow 900 for their 2700

eg 900 × 4 3600

M0A0M1A1ft

1800 said No

Answer 7200 (either M can be implied)

M0A0

M1A1ft

1350 = 20%

Answer 5400 (either M can be implied)

M0A0

M1A1ft

900 × 12 as a full method, answer 10 800 M1A1M1A1

900 × 12 as a full method with incorrect answer M1A1M1A0


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7(a)

0.56 + 0.19 + 0.14 + 0.08 or 0.97

or

1 – 0.56 – 0.19 – 0.14 – 0.08

or

100 – 56 – 19 – 14 – 8

or

100 – 97

M1

0.03 or 3% or 3

100 A1

Additional Guidance

3 without % M1A0

Embedded answer: 0.97 + 0.03 = 1 (table blank) M1A0

Table wins unless blank

7(b)

1.28 or 128% or 128

100 B1

9 400 000 ÷ 1.28 M1 oe 9 400 000 ÷ 128 × 100

7 343 750 or 7 343 800

or 7 344 000 or 7 340 000 A1

Accept 7 300 000 with working

SC2 13 055 555.(...) or 13 055 556

Additional Guidance

Condone mistakes in number of zeros for M1 and allow recovery for 3 marks

Accept answers as eg 7.34 million

For the special case allow the marks if they give full values but then round SC2

6 768 000 B0M0A0


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8(a) 1.4 × 10-2 B2

B1 0.013(8...) or 0.014 oe

or 1 × 10-2

or

B1ft ft their answer with at least 3 sf

given in standard form to 2 sf

SC1 1.9 × 10-2 or 2.2 × 10-2

8(b)

(3.9 × 10-7) ÷ (1.2 × 10-8) M1 Digits 325 imply M1

32(.5) or 3.2(5) × 10(1)

or 33 or 3.3 × 10(1) A1 SC1 0.03(0769...) or 3(.0769...) × 10-2

9(a)

Correct box plot with min 40, lower

quartile 42, median 43, upper quartile

43.5 and max 46.5 B3

B2 any four values correctly plotted

or

lower quartile 42, median 43 and

upper quartile 43.5

B1 lower quartile 42 or median 43

or upper quartile 43.5

Allow ± ½ small square tolerance

Additional Guidance

The box plot wins but if blank the stated values may gain up to B2

Mark intention throughout

Accept unconventional plots eg

line through middle of box

arrows/ dots/ longer vertical lines/ no endings on whiskers

any depth of box

any vertical alignment but not overlapping Ben’s (max B2 if it overlaps Ben’s)

Assume a box without a median line represents the LQ and UQ


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9(b)

Zoe because her inter-quartile range

is smaller

or

Zoe and her inter-quartile range = 1.5

and Ben’s = 2

B1ft

oe

Accept Zoe because her range is smaller

or

Zoe and her range = 6.5 and Ben’s = 7

ft their complete box plot

Additional Guidance

If values are quoted they must be correct, but follow through their values from a (completed) box

plot

They must be using inter-quartiIe range (IQR) or range. Ignore comments about other measures

If they do not have a complete box plot, then assume they are using the graph

Must use the words range or (inter-)quartile range – do not accept a description of the measure

If the ‘correct’ answer is seen but it does not match their box plot, please escalate the clip

Accept eg Zoe because her IQR is closer/ lower B1

10(a)

B2

oe

B1 at least two correct probabilities in the correct position

Additional Guidance

Accept decimals or percentages or equivalent fractions.

3

4 may be 0.75 or 75%

3

5may be 0.6(0) or 60%

2

5may be 0.4(0) or 40%

3

5

3

5

3

4

2

5

2

5


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10(b)

Alternative method 1

1 3 their

4 5 or

3

20

or

3 2their their

4 5 or

6

20 or

3

10

M1 oe

1 3 their

4 5 +

3 2their their

4 5 M1dep oe

9

20 or 0.45 or 45% A1ft

oe

ft their tree diagram (for probabilities < 1)


1 2 their

4 5 or

2

20 or

1

10

and

3 3their their

4 5 or

9

20

M1 oe

1 – (1 2

their4 5 +

3 3their their

4 5 ) M1dep oe

9

20 or 0.45 or 45% A1ft

oe

ft their tree diagram (for probabilities < 1)

Additional Guidance

9

20 from

3 3

4 5 (and correct tree diagram) M0M0A0

Allow up to M1 if all four combined probabilities shown next to tree diagram

and no work of further merit seen M1

Students may restart in part (b) and not use their tree diagram

Correct method seen for top, bottom or middle two probabilities M1


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11(a)

440 × 150 ÷ 1200

or 1200 ÷ 150 = 8

or 150 ÷ 1200 = 0.125 oe

M1

oe 440 ÷ 8 or 440 × 0.125

Condone 150 × [0.36, 0.37]

implied by [54, 55.5]

55 A1

Additional Guidance

Do not allow 1040 as a misread for 1200 eg

440 × 150 ÷ 1040 = 63

but there is a correct method using 1040 where the student works out that

there are 130 in the sample from the main school and works out

130 ÷ 1040 × 440 oe (which evaluated is 55)

M0A0

M1(A1)


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11(b)


160 × 150 ÷ 1200

or 150 – 75 – their 55

or 20

M1 oe eg 160 ÷ 8

Condone 150 × 0.13(...)

11 and 9

or 9 × 1200 ÷ 150

or 88 seen

M1 oe

Condone 8 × 1200 ÷ 150 with 12 or 20 seen

72 A1


2 × 1200 ÷ 150

or 2 × 8 or 16 M1 oe

(160 – their 16) ÷ 2

or 160 ÷ 2 – their 16 ÷ 2

or 88 seen

M1 oe

72 A1

Additional Guidance

Two numbers with a difference of 16 M1

Allow eg 12000 or 2000 or 2100 as a misread of 1200 for up to M2

Check table for possible creditworthy work

If they use an incorrect scale factor in (b) that follows through from (a), then escalate the clip

In Alt 1 for the second M1 accept their 9 × 1200 ÷ 150 if their 9 comes from an arithmetic error

with full method shown

11 and 9 seen even with other wrong working M2


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12

120 and 100 in correct positions in the

table B1

120 – 140 bar 4.5 large squares high B1

140 – 180 bar 1 large square high B1

Correct vertical scale or key shown Q1

Strand (ii)

1 large square = 20 ribbons oe

or 5 small squares = 4 ribbons oe

or scale of 2 per cm

Additional Guidance

Only need to show one graduation for scale but if more shown must be correct

If correct scale is shown ignore any workings on the histogram

Correct frequency on one bar is equivalent to a key as long as the scale does not contradict

Look for ‘key’ near table but do not allow it written as working in the working lines


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13


Identifying possible totals as 4, 6 and

5, 6 M1

Ignore 5, 5 and 6, 6 for M1

May be in sample space diagram or list

At least three of 4, 6 and 6, 4 and 5, 6

and 6, 5 only M1dep

3 or 4 correct totals chosen in sample space

or list (with 30 or 36 outcomes)

1 1

6 5 or 30 outcomes stated M1 Denominator of 30

4

30 or

2

15 or 0.133... or 13.3...% A1

SC2 4

36 oe (from all 4 outcomes)

SC1 36

2 oe (from 4, 6 and 5, 6)


Identifying possible totals as 4, 6 and

5, 6 M1

Ignore 5, 5 and 6, 6 for M1

May be in sample space diagram or list

Complete list of 15 pairs with only 4, 6

and 5, 6 chosen M1dep

Condone list with any of 1, 1 and 2, 2 etc

included

15 outcomes stated M1 Denominator of 15

2

15 or 0.133... or 13.3...% A1

SC2 4

36 oe (from all 4 outcomes)

SC1 36

2 oe (from 4, 6 and 5, 6)

Additional Guidance

The special cases must come from either no working or the methods stated in brackets

If a sample space or list is used the possible totals must be identified eg ringed for M1M1 but a correct numerator with a correct sample space or list may imply the correct pairs for M1M1

A sample space diagram may be incomplete if unambiguous

In any list or diagram allow one error or omission or repeat and always allow 1, 1 and 2, 2 etc

Sample space with 36 outcomes and 6 possible pairs chosen (including 5, 5

and 6, 6) is likely to lead to the answer 6

36 or

1

6

M1M0M0A0


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14


8.5 or 9.5 or

0.145 or 0.155 seen B1

9.5 ÷ 0.145 or 65.5... M1 Condone (9, 9.5] ÷ [0.145, 0.15)

65 A1 Must be using 9.5 and 0.145


8.5 or 9.5 or

0.145 or 0.155 seen B1

0.145 × 65 = 9.425

and

0.145 × 66 = 9.57

M1

Condone

[0.145, 0.15) × n = a

and

[0.145, 0.15) × (n + 1) = b

where a < 9.5 and b > 9.5

65 A1 Must be using (9.5 and) 0.145

Additional Guidance

9.49 ÷ 0.145 = 65.4...

answer 65 B1M1A0

Answer only of 65 B0M0A0

Allow conversion to millilitres throughout

9.49̇ is equivalent to 9.5 so can score full marks but do not accept use of eg 9.499 for the A mark

gcse mathematics mark scheme unit 01 - statistics and

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